Optical interpretation of special relativity and quantum mechanics

TL;DR

This paper demonstrates that relativistic and quantum mechanics can be interpreted through optical analogies by transforming space-time variables, revealing deep connections between light propagation, mechanics, and quantum phenomena.

Contribution

It introduces a novel framework linking relativistic dynamics and quantum mechanics to optical principles via variable transformations and wave equations.

Findings

Relativistic dynamics mapped to light propagation in non-homogeneous media

Quantum mechanics derived from wave equations in modified space-time

Non-relativistic quantum results emerge naturally from the theory

Abstract

The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle's trajectory through the modified space-time is thus formally equivalent to a light ray and can be derived from a mechanical equivalent of Fermat's principle. The similarities between light propagation and mechanics are then extended to quantum mechanics, showing that relativistic quantum mechanics can be derived from a wave equation in modified space-time. Non-relativistic results, such as de Broglie's wavelength, Schroedinger equation and uncertainty principle are shown to be direct consequences of the theory and it is argued that relativistic conclusions are also possible.